http://www.cnn.com/2017/11/05/us/devin-kelly-texas-church-shooting-suspect/index.html
Kelley purchased the Ruger AR-556 rifle in April 2016 from an Academy Sports & Outdoors store in San Antonio, a law enforcement official told CNN.
When Kelley filled out the background check paperwork at the store, he checked the box to indicate he didn't have disqualifying criminal history, the official said. He listed an address in Colorado Springs, Colorado when he bought the rifle, the official said.
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https://www.guntrustlawyer.com/2010/09/dishonorable-discharge-and-nfa.html
The dishonorable discharge is based on a general court-martial conviction. This means the conviction is a felony, regardless of what the underlying offense may have been. The convicted felon is banned from possessing a firearm including Title II Firearms (a Silencer, SBR, SBS, AOW, or Machine Gun).
A person who is convicted of a crime that is punishable by imprisonment for more than one year ( including a dishonorable discharge) is prohibited from possessing a firearm. Under 18 U.S.C. 922(g), a felon who is found guilty of gun possession may serve up to 10 years in prison.
If you have been convicted of a felony or a dishonorable discharge, be careful of constructive possession. You could be guilty of being in possession of a firearm if your spouse or another family or household member has a firearm that you “could” access.